Debiased estimation and variable selection under function-on-scalar linear regression models with ultrahigh-dimensional covariates subject to measurement error
Abstract
In real-world applications, data are often error-contaminated; naively applying conventional methods without accommodating the measurement error effects often yields inconsistent estimates. Biased results can be further exacerbated by the ultrahigh-dimensionality of covariates. Focusing on the widely used function-on-scalar linear regression model, this article develops new methods for simultaneous parameter estimation and variable selection with error-prone covariates that can be ultrahigh-dimensional. The proposed framework provides flexibility to handle different types of measurement error models. We rigorously establish asymptotic properties of the proposed estimators under mild conditions. Notably, the convergence rates and limiting distributions of the proposed estimators depend on the nature of measurement error. Our findings highlight the significant differences of settings with ultrahigh dimensions compared to scenarios with finite dimensions, as well as the drastically different influence of different measurement error processes. For efficient computation, we design algorithms with data-driven tuning. We evaluate the finite sample performance of the proposed method through simulation studies and a real data application, demonstrating its effectiveness in addressing the challenges posed by error-contaminated and ultrahigh-dimensional of covariates.